Problem: Simplify the following expression: $n = \dfrac{-27r - 54}{-36r + 117}$ You can assume $r \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-27r - 54 = - (3\cdot3\cdot3 \cdot r) - (2\cdot3\cdot3\cdot3)$ The denominator can be factored: $-36r + 117 = - (2\cdot2\cdot3\cdot3 \cdot r) + (3\cdot3\cdot13)$ The greatest common factor of all the terms is $9$ Factoring out $9$ gives us: $n = \dfrac{(9)(-3r - 6)}{(9)(-4r + 13)}$ Dividing both the numerator and denominator by $9$ gives: $n = \dfrac{-3r - 6}{-4r + 13}$